The Percentages Go On!

Number Theory Level 3

$\color{#3D99F6}{1\%}$ of $\color{#D61F06}{2\%}$ of $\color{#20A900}{3\%}$ of $\color{#69047E}{4\%}$ ... of $\color{fuchsia}{99\%}$ of the number $100$ .

Which of these answer choices represent the value of number as described above? Please choose the most simplified form.

\frac{99!}{100^{98}}

\frac{99!}{100^{99}}

\frac{100!}{100^{100}}

\frac{99!}{100^{100}}

\frac{100!}{100^{99}}

\frac{98!}{100^{98}}

1 solution

Feathery Studio
Jun 15, 2015

$\frac{1}{100} \times \frac{2}{100} \times \frac{3}{100} \times \frac{4}{100}... \times \frac{99}{100} \times 100 = \frac{99!}{100^{99}} \times 100 = \frac{100!}{100^{99}} = \boxed{\frac{99!}{100^{98}}}$

The Percentages Go On!

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